Methods of detecting and/or monitoring and/or evaluating the trajectory of a supersonic projectile based on detection of shock-wave produced by the projectile are known in the art. FIG. 1A schematically illustrates a projectile 10, e.g. a bullet or a shell, traveling at a supersonic speed along a trajectory 20. Projectile 10 typically generates a pressure shock-wave, commonly referred to as a sonic boom, which propagates within a conical field 12. As shown in FIG. 1A, conical field 12 is defined by a tip 14 at projectile 10 and an angle, .beta., which is determined by the following equation: EQU .beta.=sin.sup.-1 (c/v), C&lt;v (1)
wherein C is the speed of sound and v is the speed of the projectile.
In the example shown in FIG. 1A, the shock wave generated by projectile 10 is sensed by a sensor 16, for example an acoustic transducer. Since the shock-wave is confined to field 12, the shock wave is not sensed by a sensor 18 which is situated outside the boundaries of field 12. However, after a short time period, as tip 14 of field-of-view 12 advances along trajectory 20, the shock wave is sensed also by sensor 18.
FIG. 1B schematically illustrates the outputs 22 of four acoustic transducers in a vicinity of a supersonic projectile as a function of time. The transducers are positioned at different locations and, therefore, the shock wave generated by the projectile is sensed by the different transducers at different times. The magnitudes of the sensed shock waves are also position-dependent and are, therefore, different for the different transducers. As shown in FIG. 1B, each transducer output 22 is characterized by an abrupt, transient peak, as the shock wave reaches the transducer, followed by a gradual decay. The abrupt acoustic transient causing the transient peak is generally referred to as a sonic boom. The short rise time of the transient peak, typically on the order of 1 microsecond, enables very accurate determination of the time of arrival of the sonic boom at the transducer. However, determining the trajectory of the projectile based on the transducer outputs is extremely complex and, therefore, relies on physical assumptions which considerably reduce the reliability and accuracy of the system.
One common application of determining the trajectories of projectiles is in hit indication systems. In such systems, a plurality of sensors, e.g. acoustic transducers, are positioned at different locations in a vicinity of a target plane, which may be a virtual target plane. The point at which a projectile intersects the target plane is determined based on the relative times of arrival of the sonic booms at the different sensors and based on certain assumptions which introduce hit indication errors, as described below.
In some known hit indicator systems, it is assumed that the trajectory of the projectile is perpendicular to the target plane at the point of incidence. This assumption simplifies the calculations involved in determining the point of incidence at the target plane. However, when the trajectory of the projectile is substantially not perpendicular to the target plane, the accuracy of such systems is dramatically reduced. Hit indication systems based on the assumption of the trajectory being perpendicular to the target plane are described, inter alia, in U.S. Pat. Nos. 4,514,621 and 4,885,725. It should be noted that the mathematical models suggested by these references do not apply to situations in which the direction of the trajectory is not perpendicular to the target plane. Furthermore, the mathematical equations derived for these models cannot be modified to account for trajectories which are not perpendicular to the target plane.
In other known hit indicator systems, the calculations involved in determining the trajectory of the projectile at the target plane are based on the use of unique geometrical configurations of sensors. For example, in the above-mentioned '725 patent and in U.S. Pat. No. 5,241,518, the sensors are arranged in a plurality of triangular sub-array configurations, each sub-array including three sensors. A three-dimensional direction vector, normal to the shock-wave front, is calculated for each triangular sub-array, based on the relative times of arrival of the sonic booms at the three sensors of the sub-array. It is appreciated that if the direction of the trajectory is unknown, a minimum of three such triangular sub-arrays is required in order to determine the point of incidence of the trajectory at the target plane. Therefore, this approach requires the use of at least 9 sensors and imposes a geometrical constraint on the positioning of the sensors. Furthermore, not all the information obtainable from the sensors is utilized, for example, in the above-mentioned '518 patent, the relative time-delays between the different sub-arrays are not used.